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Консультация № 184097
26.09.2011, 23:37
51.74 руб.
27.09.2011, 00:37
0
8
3
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Обсуждение
27.09.2011, 08:43
общий
это ответ
Здравствуйте, Ольга Никанова!
1)(а)
После замены y=(x+1)2 получаем ряд с коэффициентами
cn=n/[(n2+1)9n]
радиус сходимости находим по формуле
R=lim|cn/cn+1=lim n((n+1)2+2)9n+1/[(n2+1)9n(n+1)]=9
следоватеьно, ряд сходится при |y|<9 или при |x+1|<3 [$8660$] -4<x<2
Проверяем сходимость на концах интервала сходимости:
при |x+1|=3 получаем ряд с общим членом an=n/(n2+1) эквивалентным 1/n. Такой ряд расходится, поэтому расходится и наш ряд
Ответ: -4<x<2
1)(а)
После замены y=(x+1)2 получаем ряд с коэффициентами
cn=n/[(n2+1)9n]
радиус сходимости находим по формуле
R=lim|cn/cn+1=lim n((n+1)2+2)9n+1/[(n2+1)9n(n+1)]=9
следоватеьно, ряд сходится при |y|<9 или при |x+1|<3 [$8660$] -4<x<2
Проверяем сходимость на концах интервала сходимости:
при |x+1|=3 получаем ряд с общим членом an=n/(n2+1) эквивалентным 1/n. Такой ряд расходится, поэтому расходится и наш ряд
Ответ: -4<x<2
Неизвестный
27.09.2011, 09:30
общий
Адресаты:
Спасибо.А вечером можете сделать 2 и 4 самое главное,в остальном более менее разобралась
27.09.2011, 10:28
общий
это ответ
Здравствуйте, Ольга Никанова!
С уважением.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
27.09.2011, 17:46
общий
Адресаты:
Спасибо Вам огромное!!! Свое обещание сдержу!!! А можно 1(б) ещё,что-то я с ним запуталась
27.09.2011, 20:51
общий
27.09.2011, 20:53
1 (б)
Коэффициенты степенного ряда cn=3n(n!)2/(2n)!
Радиус сходимости R=lim|cn/cn+1|=lim2(2n+1)/3(n+1)=4/3
Интервал сходимости: |x-8|<4/3
Сходимость в граничных точках:
имеем ряд с модулем общего члена |an|=4n(n!)2/(2n)!
величина |an|/|an+1|=(2n+1)/(2n+2)<1
Это означает, что модули общего члена ряда возрастают и поэтому не могут стремиться к нулю. Не выполнено необходимое условие сходимости и ряд в обеих граничных точках расходится.
Ответ: |x-8|<4/3
Коэффициенты степенного ряда cn=3n(n!)2/(2n)!
Радиус сходимости R=lim|cn/cn+1|=lim2(2n+1)/3(n+1)=4/3
Интервал сходимости: |x-8|<4/3
Сходимость в граничных точках:
имеем ряд с модулем общего члена |an|=4n(n!)2/(2n)!
величина |an|/|an+1|=(2n+1)/(2n+2)<1
Это означает, что модули общего члена ряда возрастают и поэтому не могут стремиться к нулю. Не выполнено необходимое условие сходимости и ряд в обеих граничных точках расходится.
Ответ: |x-8|<4/3
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